OK- here we go....I'm a lawyer, not a a mathemetician, but I'm pretty sure my numbers add up.
The difference appears to be that you are assuming a gearbox reduction of 4.2:1- the Grubee gearbox for the 4 stroke does not have that ratio. Perhaps that is the ratio for the standard 2 stroke. I don't know.
[edit] I see that the Grubee website lists the gearbox reduction as 4.2:1- that is wrong and does not even match their own numbers. They also list the final ratio as 9.29:1 with a 11 tooth to 56 tooth sprocket. I listed it as 9.3:1. 11 to 56 tooth results in 5.09 (as below), meaning for a final drive of about 9.3:1, the gearbox must be 1.83:1- and this fits with my observation of my own gearbox[/edit]
The Grubee gearbox has a reduction of 1.83 to 1 internally. The output sprocket is an 11 tooth and the wheel is 56 tooth. Therefore, that reduction is 5.09:1. That is multiplied by the gearbox reduction of 1.83:1 to get a total reduction of about 9.3:1 from crankshaft to wheel.
A 2.125" 26 inch wheel actually has an outside diameter of about 26 inches. The circumference is about 81.7 inches or 6.8 feet. In one mile, the wheel will travel 5280 feet, so it goes around 776.5 times. Multiply that by 40, becouse I was speaking of traveling 40 miles in one hour- you get 31,058.8 revolutions per hour, or, divided by 60, 517.6 revolutions of the back wheel per minute.
So- the back wheel does 517.6 rpm at 40mph- to figure the engine rpm, we just multiply by the total reduction, 9.3, and we see the engine rpm is 4,814 rpm @ 40mph. this is well within the engine's rpm range of a maximum of 7800, no load.
To anticipate someone else's question, if the rated maximum rpm of the GXH50 is 7800 rpm, why can't we get a top speed of 64 mph? There is not enough horsepower to push my large behind, the wind and the bike to the engine's maximum no-load rpm (that's why its a "no load" rpm)